因子von Neumann代数上的非线性Lie导子

张芳娟, 张建华, 陈琳, 朱新宏

数学学报 ›› 2011, Vol. 54 ›› Issue (5) : 791-802.

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数学学报 ›› 2011, Vol. 54 ›› Issue (5) : 791-802. DOI: 10.12386/A2011sxxb0081
论文

因子von Neumann代数上的非线性Lie导子

    张芳娟1, 张建华2, 陈琳2, 朱新宏3
作者信息 +

Nonlinear Lie Derivations on Factor von Neumann Algebras

    Fang Juan ZHANG1, Jian Hua ZHANG2, Lin CHEN2, Xin Hong ZHU3
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文章历史 +

摘要

M是作用在维数大于2的复可分 Hilbert空间H上的因子von Neumann代数. 证明了因子von Neumann代数M上的每一个非线性Lie 导子具有形式Aφ(A)+h(A)I, 其中φ:MM是可加的导子, h:M→C是非线性映射且对所有A,BM,有h(AB-BA)=0.  

Abstract

Let M be a factor von Neumann algebra acting on a complex separable Hilbert space H with dim H > 2. We prove that every nonlinear Lie derivation on a factor von Neumann algebra M is of the form Aφ(A)+h(A)I, where φ : MM is an additive derivation and h : M → C is a nonlinear map with h(AB-BA) = 0 for all A,BM.  

关键词

Lie导子 / 非线性 / von Neumann代数

Key words

Lie derivation / nonlinear / von Neumann algebra

引用本文

导出引用
张芳娟, 张建华, 陈琳, 朱新宏. 因子von Neumann代数上的非线性Lie导子. 数学学报, 2011, 54(5): 791-802 https://doi.org/10.12386/A2011sxxb0081
Fang Juan ZHANG, Jian Hua ZHANG, Lin CHEN, Xin Hong ZHU. Nonlinear Lie Derivations on Factor von Neumann Algebras. Acta Mathematica Sinica, Chinese Series, 2011, 54(5): 791-802 https://doi.org/10.12386/A2011sxxb0081

参考文献

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基金

国家自然科学基金资助项目(10571114);陕西省自然科学基础研究计划资助项目(2004A17)

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